How to Add Binary Numbers

Binary addition works on the same principles as decimal addition, but only uses the digits 0 and 1. This calculator allows you to add two or more binary numbers and shows each step in detail, including how carries are handled.

Binary Addition Rules

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 10 (0 carry 1)
• 1 + 1 + 1 = 11 (1 carry 1)

Example: Add 1011 + 1101

Let’s add two binary numbers:

      1011
    + 1101
    -------
     11000
    

Step-by-step:

• 1 + 1 = 10 → Write 0, carry 1
• 1 + 0 + carry = 10 → Write 0, carry 1
• 0 + 1 + carry = 10 → Write 0, carry 1
• 1 + 1 + carry = 11 → Write 1, carry 1
• Final carry = 1 → Prepend to result

Final Result: 11000

Why Use Binary Addition?

Binary arithmetic is essential in computing. CPUs, microcontrollers, and digital circuits use binary math for processing instructions, addressing memory, and more.

Common Use Cases

• Computer Architecture – ALUs perform binary addition at the hardware level.
• Digital Circuits – Full adders and half adders use binary rules.
• Programming – Bitwise operations, IP calculations, and low-level logic.

Try It Yourself!

Use the tool above to experiment with binary numbers. Add 2, 3, or even 10 binary values and understand how computers do math internally!